Numerical analysis of homoclinic orbits emanating from a Takens-Bogdanov point

Beyn W-J (1994)
IMA Journal of Numerical Analysis 14(3): 381-410.

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It is known that branches of homoclinic orbits emanate from a singular point of a dynamical system with a double zero eigenvalue (Takens-Bogdanov point). We develop a robust numerical method for starting the computation of homoclinic branches near such a point. It is shown that this starting procedure relates to branch switching. In particular, for a certain transformed problem the homoclinic predictor is guaranteed to converge to the true orbit under a Newton iteration.
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Beyn W-J. Numerical analysis of homoclinic orbits emanating from a Takens-Bogdanov point. IMA Journal of Numerical Analysis. 1994;14(3):381-410.
Beyn, W. - J. (1994). Numerical analysis of homoclinic orbits emanating from a Takens-Bogdanov point. IMA Journal of Numerical Analysis, 14(3), 381-410.
Beyn, W. - J. (1994). Numerical analysis of homoclinic orbits emanating from a Takens-Bogdanov point. IMA Journal of Numerical Analysis 14, 381-410.
Beyn, W.-J., 1994. Numerical analysis of homoclinic orbits emanating from a Takens-Bogdanov point. IMA Journal of Numerical Analysis, 14(3), p 381-410.
W.-J. Beyn, “Numerical analysis of homoclinic orbits emanating from a Takens-Bogdanov point”, IMA Journal of Numerical Analysis, vol. 14, 1994, pp. 381-410.
Beyn, W.-J.: Numerical analysis of homoclinic orbits emanating from a Takens-Bogdanov point. IMA Journal of Numerical Analysis. 14, 381-410 (1994).
Beyn, Wolf-Jürgen. “Numerical analysis of homoclinic orbits emanating from a Takens-Bogdanov point”. IMA Journal of Numerical Analysis 14.3 (1994): 381-410.
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